MinT - Information on Result #2807975

Information on Result #2807975

Linear OOA(256⁶¹, 16387, F₂₅₆, 4, 29) (dual of [(16387, 4), 65487, 30]-NRT-code), using 256¹ times duplication based on linear OOA(256⁶⁰, 16387, F₂₅₆, 4, 29) (dual of [(16387, 4), 65488, 30]-NRT-code), using

OOA 4-folding [i] based on linear OA(256⁶⁰, 65548, F₂₅₆, 29) (dual of [65548, 65488, 30]-code), using
- constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
    - discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
      - Reedâ€“Solomon code RS(253,256) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(256⁶¹, 16387, F₂₅₆, 5, 29) (dual of [(16387, 5), 81874, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁶¹, 16387, F₂₅₆, 6, 29) (dual of [(16387, 6), 98261, 30]-NRT-code)	[i]
3	Digital (32, 61, 16387)-net over F₂₅₆	[i]